Abstract
Necessary and sufficient conditions on an ordinal α are given, such thatC(α) is primary, and that the general linear group ofC(α) is contractible. In particularC(α) possesses both of these properties if α is countable.
Similar content being viewed by others
References
C. Bessaga and A. Pelczynski,Spaces of continuous functions IV, Studia Math.19 (1960), 53–62.
P. Billard,Sur la primarité des espaces C(α), to appear in Studia Math.
P. G. Casazza,James' quasi-reflexive space is primary, to appear.
S. P. Gulko and A. V. Oskin,Isomorphic classification of spaces of continuous functions on totally ordered compact sets. Functional Anal. Appl.9 (1975), 56–57.
J. Kupka,A short proof and generalization of a measure theoretic disjointization lemma, Proc. Amer. Math. Soc.45 (1974), 70–72.
K. Kuratowski,Topology I, Academic Press and PWN, Warszawa, 1966.
S. V. Kislakov,Classification of spaces of continuous functions on ordinals, Siberian Math. J.16 (1975), 226–231.
M. A. Labbé,Isomorphism of continuous function spaces, Studia Math.52, (1975), 221–231.
J. Lindenstrauss and A. Pelczynski,Contributions to the theory of the classical Banach spaces, J. Functional Analysis8 (1971), 225–249.
J. Lindenstrauss and L. Tzafriri.Classical Banach Spaces, Lecture notes in Mathematics 338, Springer-Verlag, 1973.
S. Mazurkiewicz and W. Sierpinski,Contribution à la topologie des ensembles dénombrables, Fund. Math.1 (1920), 17–27.
B. S. Mityagin,The homotopy structure of the linear group of a Banach space, Russian Math. Surveys25 (1970), 59–103.
B. S. Mityagin and I. S. Edel'shtein,Homotopy type of linear groups of two classes of Banach spaces, Functional Anal. Appl.4 (1970), 221–231.
A. Pelczynski,Projections in certain Banach spaces, Studia Math.19 (1960), 209–228.
H. P. Rosenthal,On relativity disjoint families of measures, with some applications to Banach space theory. Studia Math.37 (1970), 13–36.
Z. Semadeni,Banach spaces non-isomorphic to their cartesian squares II, Bull Acad. Polon. Sci.8 (1960), 81–84.
W. Sierpinski,Cardinal and Ordinal Numbers, PWN, Warsaw, 1965.
Author information
Authors and Affiliations
Additional information
This is a part of the first author's Ph. D. dissertation, prepared at The Ohio State University under the supervision of Professor W. B. Johnson. The first author was supported by a University Fellowship of The Ohio State University.
This author's research was partially supported by NSF Grant MPS-74-2449.
Rights and permissions
About this article
Cite this article
Alspach, D., Benyamini, Y. Primariness of spaces of continuous functions on ordinals. Israel J. Math. 27, 64–92 (1977). https://doi.org/10.1007/BF02761606
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02761606